MinT - Information on Result #1026325

Information on Result #1026325

Linear OOA(3¹⁶⁹, 59, F₃, 3, 126) (dual of [(59, 3), 8, 127]-NRT-code), using juxtaposition based on

linear OOA(3⁴⁰, 16, F₃, 3, 33) (dual of [(16, 3), 8, 34]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,14P) [i] based on function field F/F₃ with g(F) = 7 and N(F) ≥ 16, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3¹²¹, 43, F₃, 3, 92) (dual of [(43, 3), 8, 93]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3³⁷, 15, F₃, 3, 30) (dual of [(15, 3), 8, 31]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3³⁷, 16, F₃, 3, 30) (dual of [(16, 3), 11, 31]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,17P) [i] based on function field F/F₃ with g(F) = 7 and N(F) ≥ 16 (see above)
  2. linear OOA(3⁷⁶, 28, F₃, 3, 61) (dual of [(28, 3), 8, 62]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,22P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁶⁹, 59, F₃, 3, 125) (dual of [(59, 3), 8, 126]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁶⁹, 59, F₃, 3, 124) (dual of [(59, 3), 8, 125]-NRT-code)	[i]		Strength Reduction for OOAs